Liquid oxygen (LOX) for the Space Shuttle can be stored at 90 K prior to launch in

Question:

Liquid oxygen (LOX) for the Space Shuttle can be stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. Institute of Standards and Technology??s Cryogenic Division that has an effective thermal conductivity of 0.00012 W/(m K). If the outside temperature is 20?C on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.GIVENSpherical LOX tank with superinsulationTank diameter (D) = 4 mLOX temperature (TLOX) = 90 KAmbient temperature (T??) = 20?C = 293 KThermal conductivity of insulation (k) = 0.00012 W/(m K)Heat of vaporization of LOX (hfg) = 213 kJ/kgMaximum evaporation rate ( mLox ) = 0.2 kg/hASSUMPTIONSThe thickness is small compared to the sphere diameter so the problem can be considered one dimensionalSteady state conditions prevailRadiative heat loss isnegligible